As an elevator accelerates up, you will feel yourself being pulled down. In this way, one can think of the upward acceleration of the elevator as creating a gravity that pulls you down. Similarly, when the car rounds a corner, you will feel yourself being pushed outward by a force that is like a gravitational force. These forces due to the acceleration of the elevator or car are "gravitational" in the sense that they act on everything in the elevator or the car in the "same" way.

Staff: Mentor

Consider an accelerometer at rest on the ground. There is an upwards contact force and a downwards gravitational force. These two forces cancel each other, but the accelerometer reading is non zero. It detects only the upwards contact force.

Similarly, consider an accelerometer at rest in the rotating reference frame of a centrifuge. There is an inwards contact force and an outwards inertial force. These two forces cancel each other, but the accelerometer reading is non zero. It detects only the inwards contact force.

Staff: Mentor

Suppose you are in a non inertial lab which is accelerating uniformly in a direction that we will call "up".

Inside the lab you can throw an accelerometer and see that it travels on a parabolic path. Because of the motion you know it is acted on by a downwards pointing force. However, that force is not detected by the accelerometer as it reads 0 during the motion.

Because of the existence of this force which is detectable by the motion, but not measured by the accelerometer, you know that the lab's frame is non inertial.

So you are saying that an accelerometer attached to a noninertial lab that is uniformly accelerating doesn't detect the inertial force felt by a person on that lab? This is what we are discussing here.

Staff: Mentor

So you are saying that an accelerometer attached to a noninertial lab that is uniformly accelerating doesn't detect the inertial force felt by a person on that lab?

I am saying that an accelerometer does not detect inertial forces.

The circumstances don't matter. It doesn't matter if the accelerometer is at rest or moving in the non inertial frame. It doesn't matter if the frame is uniformly accelerating or undergoing some more complicated motion.

The same is true of gravity. An accelerometer does not detect gravity either. That is one of the reasons that they are considered equivalent.

You cannot "feel" inertial forces, for the same reason accelerometers cannot detect them.

I guess we must be understanding different things by inertial force.
When riding in a bus at constant rectilinear speed I consider myself not feeling any inertial forces. When the bus becomes a noninertial frame by accelerating or taking a turn I consider the forces I feel(like being pulled back or sideways respectively ) as inertial forces,hace you never felt those?

Staff: Mentor

When the bus becomes a noninertial frame by accelerating or taking a turn I consider the forces I feel(like being pulled back or sideways respectively ) as inertial forces,hace you never felt those?

What you feel is the perfectly normal contact force of the bus pushing back on you, not any "inertial force" causing you to move relative to the bus.

The bus isn't really a good example because it isn't a true inertial frame; you always have the force of the floor of the bus pushing up on you. That makes it difficult to distinguish when the push changes because of the bus turning or accelerating. For a better experiment, imagine yourself floating in a spaceship in low Earth orbit, when the engines suddenly fire for an orbit change. You won't feel any force (and an accelerometer, strapped to you, won't register any reading) at the instant the engine fires, even though, at that instant, the ship becomes a non-inertial frame and you start moving relative to it due to "inertial forces". You will only feel a force when some part of the spaceship pushes on you.

I consider the forces I feel(like being pulled back or sideways respectively ) as inertial forces,hace you never felt those?

As Peter said, the forces that you actually feel, are frame independent real contact forces and stresses in your body. That you feel them is a frame independent physical fact, so it cannot be related to frame dependent inertial forces. When you analyse the bus from an inertial frame, then there are no inertial forces anymore, but the people in the bus are still squeezed.

What you can attribute to inertial forces is the visually observed coordinate acceleration of people relative to the bus, but not the felt proper acceleration.

I guess we must be understanding different things by inertial force.
When riding in a bus at constant rectilinear speed I consider myself not feeling any inertial forces. When the bus becomes a noninertial frame by accelerating or taking a turn I consider the forces I feel(like being pulled back or sideways respectively ) as inertial forces,have you never felt those?

Peter and A.T. have already addressed this, but I would like to expand on it. Suppose you are in a very large spaceship floating in deep space. You are floating above the floor of the spaceship (there's no gravity). Now, suddenly the spaceship's rockets fire, and it starts accelerating. What do you feel? You feel nothing at all. You just start moving toward the rear of the spaceship. You don't feel any forces until you hit the floor of the spaceship. At the point, what you feel is the force of the floor slamming into you---in other words, you feel contact forces between you and the floor. There is never a time when you feel any inertial forces.